def epochs_distributed(ts,
variability=None,
threshold=0.0,
minlength=1.0,
plot=True):
"""Same as `epochs()`, but computes channels in parallel for speed.
(Note: This requires an IPython cluster to be started first,
e.g. on a workstation type 'ipcluster start')
Identify "stationary" epochs within a time series, based on a
continuous measure of variability.
Epochs are defined to contain the points of minimal variability, and to
extend as wide as possible with variability not exceeding the threshold.
Args:
ts Timeseries of m variables, shape (n, m).
variability (optional) Timeseries of shape (n, m, q), giving q scalar
measures of the variability of timeseries `ts` near each
point in time. (if None, we will use variability_fp())
Epochs require the mean of these to be below the threshold.
threshold The maximum variability permitted in stationary epochs.
minlength Shortest acceptable epoch length (in seconds)
plot bool Whether to display the output
Returns: (variability, allchannels_epochs)
variability: as above
allchannels_epochs: (list of) list of tuples
For each variable, a list of tuples (start, end) that give the
starting and ending indices of stationary epochs.
(epochs are inclusive of start point but not the end point)
"""
import distob
if ts.ndim is 1:
ts = ts[:, np.newaxis]
if variability is None:
dts = distob.scatter(ts, axis=1)
vepochs = distob.vectorize(epochs)
results = vepochs(dts, None, threshold, minlength, plot=False)
else:
def f(pair):
return epochs(pair[0], pair[1], threshold, minlength, plot=False)
allpairs = [(ts[:, i], variability[:, i]) for i in range(ts.shape[1])]
vf = distob.vectorize(f)
results = vf(allpairs)
vars, allchannels_epochs = zip(*results)
variability = distob.hstack(vars)
if plot:
_plot_variability(ts, variability, threshold, allchannels_epochs)
return (variability, allchannels_epochs)
def epochs_distributed(ts, variability=None, threshold=0.0, minlength=1.0,
plot=True):
"""Same as `epochs()`, but computes channels in parallel for speed.
(Note: This requires an IPython cluster to be started first,
e.g. on a workstation type 'ipcluster start')
Identify "stationary" epochs within a time series, based on a
continuous measure of variability.
Epochs are defined to contain the points of minimal variability, and to
extend as wide as possible with variability not exceeding the threshold.
Args:
ts Timeseries of m variables, shape (n, m).
variability (optional) Timeseries of shape (n, m, q), giving q scalar
measures of the variability of timeseries `ts` near each
point in time. (if None, we will use variability_fp())
Epochs require the mean of these to be below the threshold.
threshold The maximum variability permitted in stationary epochs.
minlength Shortest acceptable epoch length (in seconds)
plot bool Whether to display the output
Returns: (variability, allchannels_epochs)
variability: as above
allchannels_epochs: (list of) list of tuples
For each variable, a list of tuples (start, end) that give the
starting and ending indices of stationary epochs.
(epochs are inclusive of start point but not the end point)
"""
if ts.ndim <= 2:
return analyses1.epochs_distributed(
ts, variability, threshold, minlength, plot)
else:
return distob.vectorize(analyses1.epochs)(
ts, variability, threshold, minlength, plot)
def variability_fp(ts, freqs=None, ncycles=6, plot=True):
"""Example variability function.
Gives two continuous, time-resolved measures of the variability of a
time series, ranging between -1 and 1.
The two measures are based on variance of the centroid frequency and
variance of the height of the spectral peak, respectively.
(Centroid frequency meaning the power-weighted average frequency)
These measures are calculated over sliding time windows of variable size.
See also: Blenkinsop et al. (2012) The dynamic evolution of focal-onset
epilepsies - combining theoretical and clinical observations
Args:
ts Timeseries of m variables, shape (n, m). Assumed constant timestep.
freqs (optional) List of frequencies to examine. If None, defaults to
50 frequency bands ranging 1Hz to 60Hz, logarithmically spaced.
ncycles Window size, in number of cycles of the centroid frequency.
plot bool Whether to display the output
Returns:
variability Timeseries of shape (n, m, 2)
variability[:, :, 0] gives a measure of variability
between -1 and 1 based on variance of centroid frequency.
variability[:, :, 1] gives a measure of variability
between -1 and 1 based on variance of maximum power.
"""
if ts.ndim <= 2:
return analyses1.variability_fp(ts, freqs, ncycles, plot)
else:
return distob.vectorize(analyses1.variability_fp)(
ts, freqs, ncycles, plot)
def epochs_joint(ts, variability=None, threshold=0.0, minlength=1.0,
proportion=0.75, plot=True):
"""Identify epochs within a multivariate time series where at least a
certain proportion of channels are "stationary", based on a previously
computed variability measure.
(Note: This requires an IPython cluster to be started first,
e.g. on a workstation type 'ipcluster start')
Args:
ts Timeseries of m variables, shape (n, m).
variability (optional) Timeseries of shape (n, m), giving a scalar
measure of the variability of timeseries `ts` near each
point in time. (if None, we will use variability_fp())
threshold The maximum variability permitted in stationary epochs.
minlength Shortest acceptable epoch length (in seconds)
proportion Require at least this fraction of channels to be "stationary"
plot bool Whether to display the output
Returns: (variability, joint_epochs)
joint_epochs: list of tuples
A list of tuples (start, end) that give the starting and ending indices
of time epochs that are stationary for at least `proportion` of channels.
(epochs are inclusive of start point but not the end point)
"""
if ts.ndim <= 2:
return analyses1.epochs_joint(
ts, variability, threshold, minlength, plot)
else:
return distob.vectorize(analyses1.epochs_joint)(
ts, variability, threshold, minlength, plot)
def first_return_times(dts, c=None, d=0.0):
"""For an ensemble of time series, return the set of all time intervals
between successive returns to value c for all instances in the ensemble.
If c is not given, the default is the mean across all times and across all
time series in the ensemble.
Args:
dts (DistTimeseries)
c (float): Optional target value (default is the ensemble mean value)
d (float): Optional min distance from c to be attained between returns
Returns:
array of time intervals (Can take the mean of these to estimate the
expected first return time for the whole ensemble)
"""
if c is None:
c = dts.mean()
vmrt = distob.vectorize(analyses1.first_return_times)
all_intervals = vmrt(dts, c, d)
if hasattr(type(all_intervals), '__array_interface__'):
return np.ravel(all_intervals)
else:
return np.hstack([distob.gather(ilist) for ilist in all_intervals])
def first_return_times(dts, c=None, d=0.0):
"""For an ensemble of time series, return the set of all time intervals
between successive returns to value c for all instances in the ensemble.
If c is not given, the default is the mean across all times and across all
time series in the ensemble.
Args:
dts (DistTimeseries)
c (float): Optional target value (default is the ensemble mean value)
d (float): Optional min distance from c to be attained between returns
Returns:
array of time intervals (Can take the mean of these to estimate the
expected first return time for the whole ensemble)
"""
if c is None:
c = dts.mean()
vmrt = distob.vectorize(analyses1.first_return_times)
all_intervals = vmrt(dts, c, d)
if hasattr(type(all_intervals), '__array_interface__'):
return np.ravel(all_intervals)
else:
return np.hstack([distob.gather(ilist) for ilist in all_intervals])
def epochs(ts, variability=None, threshold=0.0, minlength=1.0, plot=True):
"""Identify "stationary" epochs within a time series, based on a
continuous measure of variability.
Epochs are defined to contain the points of minimal variability, and to
extend as wide as possible with variability not exceeding the threshold.
Args:
ts Timeseries of m variables, shape (n, m).
variability (optional) Timeseries of shape (n, m, q), giving q scalar
measures of the variability of timeseries `ts` near each
point in time. (if None, we will use variability_fp())
Epochs require the mean of these to be below the threshold.
threshold The maximum variability permitted in stationary epochs.
minlength Shortest acceptable epoch length (in seconds)
plot bool Whether to display the output
Returns: (variability, allchannels_epochs)
variability: as above
allchannels_epochs: (list of) list of tuples
For each variable, a list of tuples (start, end) that give the
starting and ending indices of stationary epochs.
(epochs are inclusive of start point but not the end point)
"""
if ts.ndim <= 2:
return analyses1.epochs_distributed(ts, variability, threshold,
minlength, plot)
else:
return distob.vectorize(analyses1.epochs)(ts, variability, threshold,
minlength, plot)
def variability_fp(ts, freqs=None, ncycles=6, plot=True):
"""Example variability function.
Gives two continuous, time-resolved measures of the variability of a
time series, ranging between -1 and 1.
The two measures are based on variance of the centroid frequency and
variance of the height of the spectral peak, respectively.
(Centroid frequency meaning the power-weighted average frequency)
These measures are calculated over sliding time windows of variable size.
See also: Blenkinsop et al. (2012) The dynamic evolution of focal-onset
epilepsies - combining theoretical and clinical observations
Args:
ts Timeseries of m variables, shape (n, m). Assumed constant timestep.
freqs (optional) List of frequencies to examine. If None, defaults to
50 frequency bands ranging 1Hz to 60Hz, logarithmically spaced.
ncycles Window size, in number of cycles of the centroid frequency.
plot bool Whether to display the output
Returns:
variability Timeseries of shape (n, m, 2)
variability[:, :, 0] gives a measure of variability
between -1 and 1 based on variance of centroid frequency.
variability[:, :, 1] gives a measure of variability
between -1 and 1 based on variance of maximum power.
"""
if ts.ndim <= 2:
return analyses1.variability_fp(ts, freqs, ncycles, plot)
else:
return distob.vectorize(analyses1.variability_fp)(ts, freqs, ncycles,
plot)
def cwt_distributed(ts, freqs=np.logspace(0, 2), wavelet=cwtmorlet, plot=True):
"""Continuous wavelet transform using distributed computation.
(Currently just splits the data by channel. TODO split it further.)
Note: this function requires an IPython cluster to be started first.
Args:
ts: Timeseries of m variables, shape (n, m). Assumed constant timestep.
freqs: list of frequencies (in Hz) to use for the tranform.
(default is 50 frequency bins logarithmic from 1Hz to 100Hz)
wavelet: the wavelet to use. may be complex. see scipy.signal.wavelets
plot: whether to plot time-resolved power spectrum
Returns:
coefs: Continuous wavelet transform output array, shape (n,len(freqs),m)
"""
if ts.ndim is 1 or ts.shape[1] is 1:
return cwt(ts, freqs, wavelet, plot)
import distob
vcwt = distob.vectorize(cwt)
coefs = vcwt(ts, freqs, wavelet, plot=False)
if plot:
_plot_cwt(ts, coefs, freqs)
return coefs
def cwt_distributed(ts, freqs=np.logspace(0, 2), wavelet=cwtmorlet, plot=True):
"""Continuous wavelet transform using distributed computation.
(Currently just splits the data by channel. TODO split it further.)
Note: this function requires an IPython cluster to be started first.
Args:
ts: Timeseries of m variables, shape (n, m). Assumed constant timestep.
freqs: list of frequencies (in Hz) to use for the tranform.
(default is 50 frequency bins logarithmic from 1Hz to 100Hz)
wavelet: the wavelet to use. may be complex. see scipy.signal.wavelets
plot: whether to plot time-resolved power spectrum
Returns:
coefs: Continuous wavelet transform output array, shape (n,len(freqs),m)
"""
if ts.ndim is 1 or ts.shape[1] is 1:
return cwt(ts, freqs, wavelet, plot)
import distob
vcwt = distob.vectorize(cwt)
coefs = vcwt(ts, freqs, wavelet, plot=False)
if plot:
_plot_cwt(ts, coefs, freqs)
return coefs
def epochs_joint(ts,
variability=None,
threshold=0.0,
minlength=1.0,
proportion=0.75,
plot=True):
"""Identify epochs within a multivariate time series where at least a
certain proportion of channels are "stationary", based on a previously
computed variability measure.
(Note: This requires an IPython cluster to be started first,
e.g. on a workstation type 'ipcluster start')
Args:
ts Timeseries of m variables, shape (n, m).
variability (optional) Timeseries of shape (n, m), giving a scalar
measure of the variability of timeseries `ts` near each
point in time. (if None, we will use variability_fp())
threshold The maximum variability permitted in stationary epochs.
minlength Shortest acceptable epoch length (in seconds)
proportion Require at least this fraction of channels to be "stationary"
plot bool Whether to display the output
Returns: (variability, joint_epochs)
joint_epochs: list of tuples
A list of tuples (start, end) that give the starting and ending indices
of time epochs that are stationary for at least `proportion` of channels.
(epochs are inclusive of start point but not the end point)
"""
if ts.ndim <= 2:
return analyses1.epochs_joint(ts, variability, threshold, minlength,
plot)
else:
return distob.vectorize(analyses1.epochs_joint)(ts, variability,
threshold, minlength,
plot)
def periods(dts, phi=0.0):
"""For an ensemble of oscillators, return the set of periods lengths of
all successive oscillations of all oscillators.
An individual oscillation is defined to start and end when the phase
passes phi (by default zero) after completing a full cycle.
If the timeseries of an oscillator phase begins (or ends) exactly at phi,
then the first (or last) oscillation will be included.
Arguments:
dts (DistTimeseries): where dts.shape[1] is 1 (single output variable
representing phase) and axis 2 ranges over multiple realizations of
the oscillator.
phi=0.0: float
A single oscillation starts and ends at phase phi (by default zero).
"""
vperiods = distob.vectorize(analyses1.periods)
all_periods = vperiods(dts, phi)
if hasattr(type(all_periods), '__array_interface__'):
return np.ravel(all_periods)
else:
return np.hstack([distob.gather(plist) for plist in all_periods])
def periods(dts, phi=0.0):
"""For an ensemble of oscillators, return the set of periods lengths of
all successive oscillations of all oscillators.
An individual oscillation is defined to start and end when the phase
passes phi (by default zero) after completing a full cycle.
If the timeseries of an oscillator phase begins (or ends) exactly at phi,
then the first (or last) oscillation will be included.
Arguments:
dts (DistTimeseries): where dts.shape[1] is 1 (single output variable
representing phase) and axis 2 ranges over multiple realizations of
the oscillator.
phi=0.0: float
A single oscillation starts and ends at phase phi (by default zero).
"""
vperiods = distob.vectorize(analyses1.periods)
all_periods = vperiods(dts, phi)
if hasattr(type(all_periods), '__array_interface__'):
return np.ravel(all_periods)
else:
return np.hstack([distob.gather(plist) for plist in all_periods])
# you can use the distributed array as if it were local:
print('\nmeans of each column:\n%s' % ar.mean(axis=0))
print('\nbasic slicing:\n%s' % ar[1000:1010, 5:9])
print('\nadvanced slicing:\n%s' %
ar[np.array([20, 7, 7, 9]), np.array([1, 2, 2, 15])])
# numpy computations (and ufuncs) will automatically be done in parallel:
print('\nparallel computation with distributed arrays: ar - ar \n%s' %
(ar - ar))
print('\nparallel computation with distributed arrays: np.exp(1.0j * ar)\n%s' %
np.exp(1.0j * ar))
# functions that expect ordinary arrays can now compute in parallel:
from scipy.signal import decimate
vdecimate = distob.vectorize(decimate)
result = vdecimate(ar, 10, axis=0)
print('\ndecimated ar:\n%s' % result)
# another way to write that:
result = distob.apply(decimate, ar, 10, axis=0)
print('\ndecimated ar:\n%s' % result)